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information theory 52-104

Total questions: 53

Worksheet time: 27mins

Name
Class
Date
1.

Code rate R (k information bits and n total bits) is defined as

a)

k = n/R

b)

R = k * n

c)

R = k/n

d)

n = R * k

2.

Conditional entropy H(Y|X) lies between

a)

- H(Y) and 0

b)

0 and H(Y)

c)

- H(Y) and H(Y)

d)

0 and 1

3.

Convert the message into a signal suitable for transmission over the channel of communication, referred to as …

a)

Encoding

b)

Decoding

c)

Entropy

d)

Redundancy

4.

Determine the Hamming distance for code that can detect 3 errors and correct 2 errors.

a)

6

b)

5

c)

7

d)

9

5.

Determine the Hamming distance for code that can detect 3 errors and correct 1 errors.

a)

5

b)

4

c)

6

d)

8

6.

Determine the Hamming distance for code that can detect 5 errors and correct 3 errors.

a)

9

b)

8

c)

10

d)

14

7.

Encode a string "0000" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

0000001

b)

0000111

c)

0000000

d)

0000101

8.

Encode a string "0001" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

0001010

b)

0001001

c)

0001011

d)

0001111

9.

Encode a string "0010" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

0010010

b)

0010111

c)

0010110

d)

0010100

10.

Encode a string "0011" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

0011100

b)

0011001

c)

0011101

d)

0011111

11.

Encode a string "0100" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

0100011

b)

0100110

c)

0100111

d)

0100101

12.

Encode a string "0101" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

0101101

b)

0101000

c)

0101100

d)

0101110

13.

Encode a string "0110" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

0110101

b)

0110011

c)

0110001

d)

0110000

14.

Encode a string "0111" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

0111110

b)

0111000

c)

0111010

d)

0111011

15.

Encode a string "1000" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

1000111

b)

1000100

c)

1000101

d)

1000001

16.

Encode a string "1001" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

1001111

b)

1001010

c)

1001110

d)

1001100

17.

Encode a string "1010" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

1010111

b)

1010001

c)

1010011

d)

1010010

18.

Encode a string "1011" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

1011100

b)

1011010

c)

1011000

d)

1011001

19.

Encode a string "1100" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

1100110

b)

1100000

c)

1100010

d)

1100011

20.

Encode a string "1101" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

1101101

b)

1101011

c)

1101001

d)

1101000

21.

Encode a string "1110" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

1110000

b)

1110101

c)

1110100

d)

1110110

22.

Encode a string "1111" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

1111110

b)

1111011

c)

1111111

d)

1111101

23.

The length of the message is 16 symbols and the message’s alphabet consists of 4 symbols. Find the amount of information in this message.

a)

32

b)

64

c)

80

d)

16

24.

The efficiency of the language is 0,5 and its I average is equal to 1 bit. Calculate the number of letters in this language’s alphabet?

a)

4

b)

32

c)

64

d)

16

25.

Elements of alphabets X and Y are statistically related. It is known that H(X)=4 bits and H(Y)=10 bits. What are a range of variation for a conditional entropy H(Y|X) when H(X|Y) changes from its min to max?

a)

(from 7 to 11)

b)

(from 4 to 12)

c)

(from 6 to 10)

d)

(from 6 to 11)

26.

For Hamming distance dmin and r errors in the received word, the condition to be able to detect the errors is

a)

dmin>= r+1

b)

dmin>= 2r+1

c)

dmin>= 2r+2

d)

dmin>= r+2

27.

For Hamming distance dmin and s errors in the received word, the condition to be able to correct the errors is

a)

dmin>= s+1

b)

dmin>= 2s+1

c)

dmin>= 2s+2

d)

dmin>= s+2

28.

Hamming (7,4) code can correct ___ error(s)

a)

2

b)

3

c)

1

d)

0

29.

Hamming distance can easily be found with ...

a)

XNOR operation

b)

XOR operation

c)

OR operation

d)

AND operation

30.

How does a noise affect the data?

a)

change only the 0 to 1

b)

change only the 1 to 0

c)

change the 0 to 1 and the 1 to 0

d)

None of the above

31.

How many data bits are in the (15, 11) Hamming code?

a)

11

b)

4

c)

15

d)

5

32.

How many data bits are in the (31, 26) Hamming code?

a)

26

b)

31

c)

5

d)

4

33.

How many data bits are in the (7, 4) Hamming code?

a)

4

b)

3

c)

7

d)

10

34.

How many parity bits are in the (15, 11) Hamming code?

a)

4

b)

15

c)

11

d)

5

35.

How many parity bits are in the (31, 26) Hamming code?

a)

5

b)

26

c)

31

d)

4

36.

How many parity bits are in the (7, 4) Hamming code?

a)

3

b)

4

c)

7

d)

11

37.

A Huffman code is a = 0, b = 10, c = 110, d = 1110, e = 1111. Probabilities are p(a) = 0.50, p(b) = 0.30, p(c) = 0.15, p(d) = 0.03, p(e) = 0.02. The average length of a code words is

a)

1.75 bit

b)

2.0 bit

c)

1.3 bit

d)

1.7 bit

38.

Which letter will get the shortest codeword after Huffman coding of the word «bbaacccabaac»?

a)

a

b)

b

c)

c

d)

none

39.

An alphabet consist of the letters a, b, c, d, e and f. The probability of occurrence is p(a) = 0.06, p(b) = 0.15, p(c) = 0.4 and p(d) = 0.18, p(e)=0.17, p(f)=0.04. The Huffman code is

a)

c=1,d=000,e=001,b=010,a=0110,f=0111

b)

c=0,d=111,e=110,b=101,a=1001,f=1000

c)

c=1,d=01,e=001,b=0000,a=00010,f=00011

d)

c=1,d=01,e=001,b=000,a=0010,f=00011

e)

c=0,d=101,e=110,b=101,a=1000,f=1001

40.

If k - number of bits before Hamming encoding and n - number of bits after Hamming encoding then

a)

k > n

b)

k < n

c)

k = n

d)

k = 1/2 n

41.

In digital communication system, smaller the code rate, ... are the redundant bits.

a)

less

b)

equal

c)

more

d)

unpredictable

42.

Main idea of error control codes is

a)

To add some redundancy

b)

To delete some redundancy

c)

To double all bits

d)

None of the given

43.

Noise affects ...

a)

information source

b)

receiver

c)

channel

d)

transmitter

44.

Shannon-Fano and Huffman codes are an encoding algorithms used for

a)

lossy data compression

b)

lossless data compression

c)

error correction

d)

error detection

45.

Specify the case when entropy is maximum

a)

p1=0,5 and p2=0,5

b)

p1=1 and p2=0

c)

p1=0 and p2=1

d)

p1=0,9 and p2=0,1

46.

Specify the error position in the string "0001110", if the initial string was encoded with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

i4

b)

i1

c)

i2

d)

r2

47.

Specify the error position in the string "1000110", if the initial string was encoded with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

i1

b)

i4

c)

i2

d)

i3

48.

Specify the error position in the string "1001010", if the initial string was encoded with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

r2

b)

r1

c)

r3

d)

i3

49.

Specify the error position in the string "1001100", if the initial string was encoded with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

r3

b)

r2

c)

r1

d)

no error

50.

Specify the error position in the string "1001110", if the initial string was encoded with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

r1

b)

no error

c)

r2

d)

i4

51.

Specify the error position in the string "1001111", if the initial string was encoded with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

r1

b)

r3

c)

r2

d)

i4

52.

Specify the error position in the string "1011110", if the initial string was encoded with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

i1

b)

i3

c)

i2

d)

i4

53.

Specify the error position in the string "1101110", if the initial string was encoded with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

i1

b)

i2

c)

i3

d)

i4

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